Hi, I'm looking for the method to get the Rife vincent window or other windows constant value. Take for example Blackman window which has below equation: w(n)=0.42-0.5cos(2*pi*n/N)+0.08cos(4*pi*n/N), 0<=n<=N where the constant a0=0.42,a1=0.5,a2=0.08 -> How actually these constant being define for this type of window or other type of windows. Thanks.
Four item cosine window constant derivation
Started by ●October 25, 2007
Reply by ●October 25, 20072007-10-25
On Oct 25, 6:31 am, "boon" <boon-chun_...@agilent.com> wrote:> Hi, > I'm looking for the method to get the Rife vincent window or other > windows constant value. Take for example Blackman window which has below > equation: > w(n)=0.42-0.5cos(2*pi*n/N)+0.08cos(4*pi*n/N), 0<=n<=N > where the constant a0=0.42,a1=0.5,a2=0.08 -> How actually these constant > being define for this type of window or other type of windows. > > Thanks.boon Two classic papers that discuss the design of such cosine-summed windows are: On the use of windows for harmonic analysis with the discrete Fourier transform Harris, F.J. Proceedings of the IEEE Publication Date: Jan. 1978 Volume: 66, Issue: 1 On page(s): 51- 83 Some windows with very good sidelobe behavior IEEE Trans. Acoust., Speech, Signal Processing, vol. 29, pp. 84 - 91, February 1981 Albert H. Nuttall The Nuttall paper includes some corrections to the Harris paper. The example you give is the "two digit rounded" version of "three-term Blackman". Unfortunately, Harris gives the sidelobe rejection of the exact version (unrounded) as -51 dB which Nuttall corrects as -68.24 dB. Blackman and Tukey published the rounded version as "R. Blackman's not very serious proposal". Unfortunately, Harris and others have maligned Blackman by applying his name to the rounded version as a common usage, If you find the rounded version preferable in performance to the exact, you will probably find Nuttall's "3-term with continuous 1st derivative" is a few dB better as it is an optimized version. Good Luck! Dale B. Dalrymple http://dbdimages.com http://stores.lulu.com/dbd
Reply by ●October 31, 20072007-10-31
>On Oct 25, 6:31 am, "boon" <boon-chun_...@agilent.com> wrote: >> Hi, >> I'm looking for the method to get the Rife vincent window or other >> windows constant value. Take for example Blackman window which hasbelow>> equation: >> w(n)=0.42-0.5cos(2*pi*n/N)+0.08cos(4*pi*n/N), 0<=n<=N >> where the constant a0=0.42,a1=0.5,a2=0.08 -> How actually theseconstant>> being define for this type of window or other type of windows. >> >> Thanks. > >boon > >Two classic papers that discuss the design of such cosine-summed >windows are: > >On the use of windows for harmonic analysis with the discrete Fourier >transform >Harris, F.J. Proceedings of the IEEE >Publication Date: Jan. 1978 >Volume: 66, Issue: 1 >On page(s): 51- 83 > >Some windows with very good sidelobe behavior >IEEE Trans. Acoust., Speech, Signal Processing, vol. 29, pp. 84 - 91, >February 1981 >Albert H. Nuttall > >The Nuttall paper includes some corrections to the Harris paper. > >The example you give is the "two digit rounded" version of "three-term >Blackman". Unfortunately, Harris gives the sidelobe rejection of the >exact version (unrounded) as -51 dB which Nuttall corrects as -68.24 >dB. Blackman and Tukey published the rounded version as "R. Blackman's >not very serious proposal". Unfortunately, Harris and others have >maligned Blackman by applying his name to the rounded version as a >common usage, If you find the rounded version preferable in >performance to the exact, you will probably find Nuttall's "3-term >with continuous 1st derivative" is a few dB better as it is an >optimized version. > >Good Luck! > >Dale B. Dalrymple >http://dbdimages.com >http://stores.lulu.com/dbd > >Hi Dale,Thanks for your information. The reason of wanted to know how is the four item cosine constant being defined is because inside the paper named ANALYSIS BASED ON INTERPOLATING WINDOWED FFT ALGORITHM mentioned Rife–Vincent (III) type 4 window is a four item cosine window, the four item cosine constant are a0=1;a1=1.43596;a2=0.49754;a3=0.06158. If I would like to get the type 5 class III Rife vincent then I must know how those constant being defined. As I know but putting the proper zero in the sinc response you will get those constant. But I have no idea how to properly select the zero location for higher type of Rife vincent windows.>
